it would make sense, right, for the continuous function of i to the power of (2 * theta)/π to be a circle in the complex numbers

this would make all complex numbers representable as

q * (i^r)

for q, r drawn from the reals

(but only if it makes sense to have continuous powers of i and they make sense to characterize as I have)

now that I have definitively NOT answered the question "what happens when you raise i to any real-valued power," what happens when you raise i to any complex-valued power?

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